Computational fluid dynamics concentration profiles

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

Computational fluid dynamic (CFD) calculations were performed to give the Pd concentration profile in a nanopore of the oxide catalyst carrier layer [283]. For wet chemical deposition most of the catalyst was deposited in the pore mouth, in the first 4 pm of the pore. Thus, most of the hydrogenation reaction is expected to occur in this location. For electrochemical deposition, large fractions of the catalyst are located... 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

Kashid et al. studied the fiow patterns within the slugs and mass transfer between two consecutive slugs in liquid-liquid slug flow using a finite element-based computational fluid dynamics (CFD) model [51]. The model equations are implemented in the open-source software FEATFLOW (www.featflow.de). Figure 12.18 shows snapshots of the concentration profiles of the extract (acetic acid). These results are compared with experimental results and are consistent with them. 

Solving the full Navier-Stokes equations in the channels requires a rigorous computational fluid dynamics (CFD) simulation. During transient operation, such as start-up and shut-down, the flow fields can have a significant effect on the concentration and temperature profiles in the system. Under normal operation, it may be desirable to assume fuUy developed laminar flow to reduce the computational time and quickly estimate flow parameters based on fluid dynamics correlations. 

The other form of mathematical model is the more rigorous computational fluid dynamics (CFD) approach that solves the complete three-dimensional conservation equations. These methods have been applied with encouraging results (Britter, 1995 Lee et al. 1995). CFD solves approximations to the fundamental equations, with the approximations being principally contained within the turbulence models—the usual approach is to use the K-e theory. The CFD model is typically used to predict the wind velocity fields, with the results coupled to a more traditional dense gas model to obtain the concentration profiles (Lee et al., 1995). The problem with this approach is that substantial definition of the problem is required in order to start the CFD computation. This includes detailed initial wind speeds, terrain heights, structures, temperatures, etc. in 3-D space. The method requires moderate computer resources. 

Over the last decades, the application of computational fluid dynamics (CFD) to study the velocity and temperature profiles in packed column has been frequently reported [1-5]. However, for the prediction of concentration profile, the method commonly employed is by guessing an empirical turbulent Schmidt number Sc, or by using experimentally determined turbulent mass diffusivity D, obtained by using the inert tracer technique under the condition of no mass transfer [6, 7]. Nevertheless, the use of such empirical methods of computation, as pointed out in Chap. 3, is unreliable and not always possible. To overcome these drawbacks, the development of rigorous mathematical model is the best choice. 

Equation (3) provides details of gas flow movements. The full treatment requires a rigorous computational fluid dynamics (CFD) tool. Startup and transient processes as well as variations in certain operating parameters may have a sizeable effect on flow and concentration profiles, but the effect on overall electrochemical performance of the cell is not necessarily of the same order. Sometimes it is desirable to make a simplification such as assuming laminar flow to reduce the computation cost and allow quick estimates of certain flow properties. For example, the pressure drop of a laminar flow through a channel can be estimated as... 

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